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In this paper, we study the problem of jointly routing and scheduling traffic in an energy harvesting network. To this end, we leverage stochastic dual descent methods to propose a generalization of the well-known backpressure algorithm to energy harvesting networks. We name this policy energy harvesting backpressure (EH-BP) and show that it satisfies the fundamental property of backpressure-type algorithms. Namely, if given data arrival rates can be supported by given energy arrival rates and some routing-scheduling policy, they can be supported by the EH-BP policy. Numerical results attest to the properties of the proposed policy. ; Grant numbers : This work was partially supported by the Catalan government under grant SGR2014-1567; the Spanish government under grant TEC2013-44591-P (INTENSYV), and grant PCIN-2013-027 (E-CROPS).